Only the function represented by graph has an inverse function.

Only the function represented by graph 2 has an inverse function

Step-by-step explanation:

* Lets explain the inverse of the function

- The Function is a relation between x-coordinates and the y-

 coordinates of the order pairs under the condition every

 x-coordinate has only one y-coordinate

- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-

 coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,

 (2 , 5)} not a function because the x-coordinate 2 has two y-

 coordinates 3 and 5

- We use the vertical line to test the graph is function or not, if

 the vertical line intersects the graph in one point then the

 graph is function if intersects it in more than one point then the

 graph is not function

- We have two types of function one-to-one function and

 many-to-one function

# one-to-one function means every x-coordinate has only 1 y-coordinate

# many-to-one function means some x-coordinates have only 1

  y-coordinate

- We find the inverse function by switching x and y, then one-to-

 one function has inverse but many-to-one has not inverse

 because when we switched x and y it will be one-to-many

 means one x-coordinate has many y-coordinates and this is not

 a function

- We use the horizontal line to test the graph of the function has

 inverse or not, if the horizontal line intersects the graph in one

 point then the function of the graph has inverse if it intersects

 the graph in more than one point ,then the function of the  

 graph has no inverse

* Now lets test all the graphs by using the horizontal line

# graph 1

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 1 has no inverse

# graph 2

∵ The horizontal line cuts the graph in just 1 point

∴ The function of graph 2 has inverse

# graph 3

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 3 has no inverse

# graph 4

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 4 has no inverse

* Only the function represented by graph 2 has an inverse function

it has 4

step-by-step explanation:

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°